{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-11-11T07:58:02.106965Z",
     "start_time": "2025-11-11T07:58:01.608466Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pylab as plt"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-11T07:59:46.295582Z",
     "start_time": "2025-11-11T07:59:46.239833Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def step_function(x):\n",
    "    return np.array(x > 0, dtype=int)\n",
    "x=np.arange(-5.0, 5.0, 0.1)\n",
    "y=step_function(x)\n",
    "plt.plot(x, y)\n",
    "plt.show()\n"
   ],
   "id": "8020e3013ee9b8a3",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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kwtkOJEVlBPLjdAeSojIC+XG2A2mGEQ2skA1hBEhzNo1700A2hBEgKW6UB/kRRoBEl4MXRiAXwgiQaAOrMAK5EEaAJMNImzAC2RBGgCQbWFvMpoFsCCNAmpWRVmEEciGMAEmGEZURyIcwAiRFzwjkRxgBkmI2DeRHGAGSIoxAfoQRICmWg4f8CCNAMrq6ujSwQoaEESAZ3TmkpIEV8iGMAMnorNd7/9wijEA2hBEgGTtlEZURyIgwAiRZGdHACvkQRoAkKyPCCORDGAGSm9ZbaDWbBrIhjADJXaYpcogGVsiHMAIkd5lGVQTyIowAyVVG9ItAXoQRIL3KiDACWRFGgGSojECehBEgGXU3yYMs7VEYWbx4cYwdOzaGDh0aU6dOjZUrV+7WcbfccksMGjQoTjvttD35sUCT6+y+OY3VVyEvDYeRpUuXxty5c2PhwoWxevXqmDBhQsyYMSM2bNjwisc99dRT8bnPfS4+8IEPvJbxAk3MHXshTw2Hkeuuuy7OOeecmDNnThx11FGxZMmSOPDAA+Omm27a5TG1Wi3OOOOMuOKKK+Id73jHax0z0ORhxGUayEtDYWTHjh2xatWqmD59+r+/QUtLub1ixYpdHvelL30pDjnkkDjrrLN26+ds3749tmzZ0ucBND9hBPLUUBjZtGlTWeUYOXJkn/3F9rp16/o95r777osbb7wxbrjhht3+OR0dHTF8+PDeR3t7eyPDBAYoYQTytE9n02zdujXOPPPMMoiMGDFit4+bP39+bN68ufexdu3afTlMIBHCCOSprZEnF4GitbU11q9f32d/sT1q1KiXPf/Pf/5z2bh66qmn9u6rd68j0NbWFo8//ngcfvjhLztuyJAh5QPINIxoYIWsNFQZGTx4cEyaNCmWL1/eJ1wU29OmTXvZ88eNGxd/+MMf4qGHHup9fPSjH42TTjqp/LPLL0B/d+1VGYG8NFQZKRTTemfPnh2TJ0+OKVOmxKJFi2Lbtm3l7JrCrFmzYsyYMWXfR7EOyfjx4/scf9BBB5VfX7ofwGUayFPDYWTmzJmxcePGWLBgQdm0OnHixFi2bFlvU+uaNWvKGTYAexpGLHoGeRnU1dVdF01YMbW3mFVTNLMOGzas6uEA+8j/fGRdfOaHq+LYtx0Ut/2346seDrCfPr+VMIBkqIxAnoQRILkGVsvBQ16EESC9ykirMAI5EUaAZLhRHuRJGAGS0alnBLIkjADJqFtnBLIkjADJVUaEEciLMAIko245eMiSMAIko7OmgRVyJIwAyVVGNLBCXoQRILmekRZhBLIijADJsBw85EkYAZILIxpYIS/CCJAMYQTyJIwA6U3tNZsGsiKMAAkueuatCXLijAcSXA6+6pEA+5NTHkiGygjkyRkPJNjAWvVIgP3JKQ8kGEa8NUFOnPFAMmpm00CWhBEgGbXuG+W1tQojkBNhBEiuMuKuvZAXYQRIhgZWyJNTHkiGBlbIkzMeSC+MuEoDWRFGgPTCiOs0kBVnPJDeCqwaWCErwgiQ3F1721qEEciJMAIkd5mmRRiBrAgjQHJhRGUE8iKMAMlQGYE8CSNAMlRGIE/CCJAMy8FDnoQRILmpvSojkBdhBEhGvXc5eGEEciKMAOkteiaMQFaEESAZKiOQJ2EESEZnvV5+FUYgL8IIkIzuwogwApkRRoDkKiOm9kJehBEgGd1ZxNReyIwwAiRDzwjkSRgBklHrrowII5AXYQRIRk1lBLIkjADJ3ShPGIG8CCNAelN7zaaBrAgjQDI0sEKehBEguam9wgjkRRgBkquMWGcE8iKMAEno6urq7RlpEUYgK8IIkNRMmoLKCORFGAGSUOv6dxhRGYG8CCNAElRGIF/CCJBcGHHXXsiLMAIkF0ZM7YW87FEYWbx4cYwdOzaGDh0aU6dOjZUrV+7yuTfccEN84AMfiDe96U3lY/r06a/4fCBPfcKIyghkpeEwsnTp0pg7d24sXLgwVq9eHRMmTIgZM2bEhg0b+n3+3XffHaeffnr89re/jRUrVkR7e3ucfPLJ8cwzz+yN8QNNFkaKHKKBFfIyqKuY3N+AohJy3HHHxTe/+c1yu16vlwHjggsuiHnz5r3q8bVarayQFMfPmjVrt37mli1bYvjw4bF58+YYNmxYI8MFBoi/bv5nTOv4X/G61kHxp698pOrhAHvB7n5+N1QZ2bFjR6xataq81NL7DVpayu2i6rE7nn/++XjhhRfi4IMP3uVztm/fXv4COz+A5tZZe/H/RZpXIT8NhZFNmzaVlY2RI0f22V9sr1u3bre+x6WXXhqjR4/uE2heqqOjo0xSPY+i8gI0t3p3kda0XsjPfp1N89WvfjVuueWWuO2228rm112ZP39+WdLpeaxdu3Z/DhOoQGd3z4h+EchPWyNPHjFiRLS2tsb69ev77C+2R40a9YrHXnPNNWUY+c1vfhPHHHPMKz53yJAh5QPIR707jKiMQH4aqowMHjw4Jk2aFMuXL+/dVzSwFtvTpk3b5XFXX311XHnllbFs2bKYPHnyaxsx0NTLwVtjBPLTUGWkUEzrnT17dhkqpkyZEosWLYpt27bFnDlzyr8vZsiMGTOm7PsofO1rX4sFCxbEzTffXK5N0tNb8oY3vKF8AOzcwCqMQH4aDiMzZ86MjRs3lgGjCBYTJ04sKx49Ta1r1qwpZ9j0+Pa3v13Owvn4xz/e5/sU65R88Ytf3Bu/A9BEDawWPIP8NBxGCueff3752NUiZzt76qmn9mxkQJYNrK2twgjkxr1pgKQaWFVGID/CCJBWZUTPCGRHGAHSqowII5AdYQRIrDLibQly46wHEltnpOqRAPub0x5IQq1nnRENrJAdYQRIghVYIV/CCJCEmgZWyJYwAiRBGIF8CSNAEoQRyJcwAiQWRrwtQW6c9UBaDawKI5AdYQRIgsoI5MtZDyQWRqoeCbC/Oe2BpMJIm8oIZMdZDyQVRlrMpoHsCCNAYpURYQRyI4wASc2maXFvGsiOMAIkQWUE8iWMAEnQMwL5EkaAJHSqjEC2hBEgCXX3poFsCSNAUpURDayQH2EESEK9ezZNm5vTQHaEESAJnTWVEciVMAKkVRnRMwLZEUaAJHTW6+VXU3shP8IIkITai1lEZQQyJIwASTC1F/IljABJTe0VRiA/wgiQVANrq9k0kB1hBEiCygjkSxgBkqBnBPIljABJTe0VRiA/wgiQ1NReYQTyI4wASaipjEC2hBEgCd23pjGbBjIkjABJUBmBfAkjQBJqZtNAtoQRIAnCCORLGAGSIIxAvoQRIK0wooEVsiOMAEmo9dybplUYgdwII0Bai56pjEB2hBEgqam9bXpGIDvCCJBUz0iLMALZEUaApMKIygjkRxgBkmpgVRmB/AgjQBJq3TenURmB/AgjQFqVEbNpIDvCCJBWz4h1RiA7wgiQBCuwQr6EESAJne5NA9kSRoAk1IURyJYwAiRVGdHACvkRRoAk1Ltn02hghfzsURhZvHhxjB07NoYOHRpTp06NlStXvuLzf/rTn8a4cePK5x999NFx55137ul4gWbvGVEZgew0HEaWLl0ac+fOjYULF8bq1atjwoQJMWPGjNiwYUO/z7///vvj9NNPj7POOisefPDBOO2008rHww8/vDfGDzRJv0h3YUTPCGRoUFdXz1vA7ikqIccdd1x885vfLLfr9Xq0t7fHBRdcEPPmzXvZ82fOnBnbtm2LX/3qV7373vve98bEiRNjyZIlu/Uzt2zZEsOHD4/NmzfHsGHDGhkuMAC8UKvHEZf/j/LPDy34YBx04OCqhwTsBbv7+d3WyDfdsWNHrFq1KubPn9+7r6WlJaZPnx4rVqzo95hif1FJ2VlRSbn99tt3+XO2b99ePnb+ZfaFG+/7S/zn/3t+n3xvoPGZNAWVEchPQ2Fk06ZNUavVYuTIkX32F9uPPfZYv8esW7eu3+cX+3elo6MjrrjiitjX7vi/z8bqNc/t858D7J4hbS0xuE1fPeSmoTCyvxSVl52rKUVlpLgUtLf9l0mHxrTD37zXvy+wZ44be3AMaWutehhAymFkxIgR0draGuvXr++zv9geNWpUv8cU+xt5fmHIkCHlY187Y+rb9/nPAABeWUP10MGDB8ekSZNi+fLlvfuKBtZie9q0af0eU+zf+fmFu+66a5fPBwDy0vBlmuLyyezZs2Py5MkxZcqUWLRoUTlbZs6cOeXfz5o1K8aMGVP2fRQuvPDCOOGEE+Laa6+NU045JW655ZZ44IEH4vrrr9/7vw0A0PxhpJiqu3HjxliwYEHZhFpM0V22bFlvk+qaNWvKGTY93ve+98XNN98cn//85+Oyyy6LI444opxJM378+L37mwAAeawzUgXrjADAwLO7n9/m0AEAlRJGAIBKCSMAQKWEEQCgUsIIAFApYQQAqJQwAgBUShgBAColjAAAA2s5+Cr0LBJbrOQGAAwMPZ/br7bY+4AII1u3bi2/tre3Vz0UAGAPPseLZeEH9L1p6vV6PPvss/HGN74xBg0aFLkrkmYRzNauXetePfuY13r/8VrvP17r/Sf317qrq6sMIqNHj+5zE90BWRkpfoFDDz206mEkp/iHneM/7ip4rfcfr/X+47Xef3J+rYe/QkWkhwZWAKBSwggAUClhZAAaMmRILFy4sPzKvuW13n+81vuP13r/8VrvngHRwAoANC+VEQCgUsIIAFApYQQAqJQwAgBUShhpEtu3b4+JEyeWK9Q+9NBDVQ+n6Tz11FNx1llnxWGHHRYHHHBAHH744WWH/I4dO6oeWlNYvHhxjB07NoYOHRpTp06NlStXVj2kptTR0RHHHXdcuZr1IYccEqeddlo8/vjjVQ+r6X31q18t35svuuiiqoeSLGGkSVxyySXlcrvsG4899lh5W4LvfOc78cgjj8TXv/71WLJkSVx22WVVD23AW7p0acydO7cMd6tXr44JEybEjBkzYsOGDVUPrencc889cd5558Xvfve7uOuuu+KFF16Ik08+ObZt21b10JrW73//+/J945hjjql6KGkrpvYysN15551d48aN63rkkUeKadpdDz74YNVDysLVV1/dddhhh1U9jAFvypQpXeedd17vdq1W6xo9enRXR0dHpePKwYYNG8r3jHvuuafqoTSlrVu3dh1xxBFdd911V9cJJ5zQdeGFF1Y9pGSpjAxw69evj3POOSd++MMfxoEHHlj1cLKyefPmOPjgg6sexoBWXOZatWpVTJ8+vc+9qIrtFStWVDq2XP4NF/w73jeKKtQpp5zS5983A/hGefSvWK/u05/+dJx77rkxefLksq+B/eOJJ56Ib3zjG3HNNddUPZQBbdOmTVGr1WLkyJF99hfbxaUx9p3ismPRw3D88cfH+PHjqx5O07nlllvKy47FZRpencpIgubNm1c2O73So3ijLj4Mi1szz58/v+ohN/1rvbNnnnkmPvShD8UnPvGJsioFA/V/7Q8//HD5ocnetXbt2rjwwgvjxz/+cdmUzauzHHyCNm7cGH/7299e8TnveMc74pOf/GT88pe/LD8wexT/y2xtbY0zzjgjfvCDH+yH0ebxWg8ePLj887PPPhsnnnhivPe9743vf//75SUFXttlmuLy4q233lrO7Ogxe/bseO655+LnP/95peNrVueff3752t57773lDDH2rttvvz0+9rGPle/FO783F+/VxXtGMftx579DGBnQ1qxZE1u2bOndLj4oi1kIxRt7MT3y0EMPrXR8zaaoiJx00kkxadKk+NGPfuTNZC8p/q1OmTKlrPT1XD5429veVn5gFpUr9p7i7f6CCy6I2267Le6+++444ogjqh5SUyoq1k8//XSffXPmzIlx48bFpZde6rJYP/SMDGDFG/bO3vCGN5RfizUwBJG9H0SKisjb3/72sk+kqKj0GDVqVKVjG+iKab1FJaToeypCyaJFi8qppsWbN3v/0szNN99cVkWKtUbWrVtX7h8+fHi5fg57R/HavjRwvP71r483v/nNgsguCCOwG4o1GYqm1eLx0qCnuPjazJw5swx3CxYsKD8ci8X7li1b9rKmVl67b3/72+XXIljv7Hvf+17ZDA9VcZkGAKiU7jsAoFLCCABQKWEEAKiUMAIAVEoYAQAqJYwAAJUSRgCASgkjAEClhBEAoFLCCABQKWEEAKiUMAIARJX+Py+/15SHRWMcAAAAAElFTkSuQmCC"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 2
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-11T08:01:29.349080Z",
     "start_time": "2025-11-11T08:01:29.309322Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "x=np.arange(-5.0, 5.0, 0.1)\n",
    "y=sigmoid(x)\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ],
   "id": "af89e7f4b68c9f2f",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 3
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-11T08:05:14.988764Z",
     "start_time": "2025-11-11T08:05:14.938990Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def relu(x):\n",
    "    return np.maximum(0,x)\n",
    "x=np.arange(-5.0, 5.0, 0.1)\n",
    "y=relu(x)\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ],
   "id": "86d03170b0fc610",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 4
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-11T09:29:47.699986Z",
     "start_time": "2025-11-11T09:29:47.685814Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def softmax(a):\n",
    "    c = np.max(a)\n",
    "    exp = np.exp(a-c)\n",
    "    sum_exp = np.sum(exp)\n",
    "    return exp/sum_exp\n",
    "a=np.array([0.3,2.9,4.0])\n",
    "y=softmax(a)\n",
    "print(y)\n"
   ],
   "id": "bdb3a8418acd8efd",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.01821127 0.24519181 0.73659691]\n"
     ]
    }
   ],
   "execution_count": 6
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
